Integer Programming from Quantum Annealing and Open Quantum Systems

TL;DR

This paper develops a quantum annealing algorithm for solving integer linear programming problems, analyzes hardware limitations, and demonstrates potential improvements through optimized annealing schedules and simulations.

Contribution

It introduces a formalism for mapping ILP problems to quantum annealers and models the anneal process, including effects of decoherence and localization.

Findings

Algorithm outperforms random guessing on small problems

Optimized annealing schedules reduce decoherence effects

Simulations suggest quantum effects contribute to improvements

Abstract

While quantum computing proposes promising solutions to computational problems not accessible with classical approaches, due to current hardware constraints, most quantum algorithms are not yet capable of computing systems of practical relevance, and classical counterparts outperform them. To practically benefit from quantum architecture, one has to identify problems and algorithms with favorable scaling and improve on corresponding limitations depending on available hardware. For this reason, we developed an algorithm that solves integer linear programming problems, a classically NP-hard problem, on a quantum annealer, and investigated problem and hardware-specific limitations. This work presents the formalism of how to map ILP problems to the annealing architectures, how to systematically improve computations utilizing optimized anneal schedules, and models the anneal process through a simulation. It illustrates the effects of decoherence and many body localization for the minimum dominating set problem, and compares annealing results against numerical simulations of the quantum architecture. We find that the algorithm outperforms random guessing but is limited to small problems and that annealing schedules can be adjusted to reduce the effects of decoherence. Simulations qualitatively reproduce algorithmic improvements of the modified annealing schedule, suggesting the improvements have origins from quantum effects.